8/x-5=x+2

Solution for 8/x-5=x+2 equation:

8/x-5=x+2

We move all terms to the left:

8/x-5-(x+2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8/x-x-2-5=0

We multiply all the terms by the denominator


-x*x-2*x-5*x+8=0

We add all the numbers together, and all the variables

-7x-x*x+8=0

Wy multiply elements

-1x^2-7x+8=0

a = -1; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-1)·8
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-1}=\frac{16}{-2}
=-8
$